Integral Calculus: JEE Main 2022 Mathematics question

For any real number $x$, let $[x]$ denote the largest integer less than equal to $x$. Let $f$ be a real valued function defined on the interval $[-10,10]$ by $f(x)=\left\{\begin{array}{l}x-[x], \text { if }[x] \text { is odd } \\ 1+[x]-x, \text { if }[x] \text { is even } .\end{array}\right.$ Then the value of $\frac{\pi^{2}}{10} \int_{-10}^{10} f(x) \cos \pi x \,d x$ is :